Details

Time bar (total: 5.9s)

sample34.0ms

Algorithm
intervals
Results
6.0ms321×body80nan
6.0ms47×body1280valid
5.0ms50×body640valid
3.0ms124×body80valid
2.0ms25×body320valid
0.0ms10×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0116
1146
2146

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.9b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
2.7b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
75×*-un-lft-identity
73×add-sqr-sqrt
69×times-frac
50×sqrt-prod
42×add-cube-cbrt
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
8×add-exp-log add-cbrt-cube distribute-lft-out
6×associate-/l* add-log-exp
5×pow1
4×sqrt-div div-inv
2×cbrt-undiv frac-2neg flip3-+ div-exp clear-num associate-/r/ flip-+
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log frac-sub flip--
Counts
4 → 133
Calls
4 calls:
9.0ms
(sqrt (+ x 1.0))
12.0ms
(/ 1.0 (sqrt (+ x 1.0)))
6.0ms
(/ 1.0 (sqrt x))
59.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series257.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(sqrt (+ x 1.0))
66.0ms
(/ 1.0 (sqrt (+ x 1.0)))
38.0ms
(/ 1.0 (sqrt x))
122.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify49.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04431097
114341038
25001992

prune298.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 20.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
0.3b
(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
0.5b
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
2.7b
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite280.0ms

Algorithm
rewrite-expression-head
Rules
362×times-frac
331×*-un-lft-identity
258×add-sqr-sqrt
180×sqrt-prod
174×add-cube-cbrt
88×distribute-lft-out
67×swap-sqr
49×associate-*r* associate-*l*
30×add-exp-log add-cbrt-cube
19×div-inv
18×pow1 frac-sub unswap-sqr
16×difference-of-squares
14×frac-times associate-*r/ associate-*l/ associate-/r*
11×associate-/r/ associate-/l/
9×cbrt-undiv div-exp
8×sqrt-div prod-exp cbrt-unprod
6×add-log-exp
5×flip3-+ flip-+
4×associate-/l*
2×pow2 flip3-- pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up flip--
1×sub-neg frac-2neg diff-log div-sub frac-add clear-num
Counts
4 → 354
Calls
4 calls:
63.0ms
(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
139.0ms
(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
34.0ms
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
17.0ms
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

series437.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
332.0ms
(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
28.0ms
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
54.0ms
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

simplify78.0ms

Algorithm
egg-herbie
Counts
366 → 366
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
015935895
150015420

prune709.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
0.3b
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
2.2b
(- (+ x 1.0) x)

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
303×*-un-lft-identity
296×times-frac
124×sqrt-prod
117×distribute-lft-out
108×add-sqr-sqrt
106×add-cube-cbrt
37×add-exp-log add-cbrt-cube
35×associate-/r/
34×div-inv
30×associate-*l/
27×associate-/r*
17×flip3-+ flip-+
15×cbrt-undiv div-exp
13×associate-/l*
9×prod-exp cbrt-unprod add-log-exp
4×pow1
3×frac-2neg clear-num
2×sqrt-div diff-log distribute-lft-out--
1×sub-neg flip3-- frac-add associate--l+ sum-log flip-- associate-/l/ difference-of-squares
Counts
4 → 248
Calls
4 calls:
11.0ms
(/ 1.0 (sqrt (+ x 1.0)))
6.0ms
(/ 1.0 (sqrt x))
146.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
36.0ms
(- (+ x 1.0) x)

series563.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(/ 1.0 (sqrt (+ x 1.0)))
35.0ms
(/ 1.0 (sqrt x))
457.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
1.0ms
(- (+ x 1.0) x)

simplify63.0ms

Algorithm
egg-herbie
Counts
260 → 260
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012493999
150013639

prune493.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x))
0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
6.0b
(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
298×*-un-lft-identity
297×times-frac
124×sqrt-prod
116×distribute-lft-out
106×add-sqr-sqrt add-cube-cbrt
58×add-exp-log add-cbrt-cube
37×associate-/r/
35×div-inv
32×associate-*l/
28×associate-/r*
21×cbrt-undiv div-exp
18×flip3-+ prod-exp cbrt-unprod flip-+
14×associate-/l*
4×pow1 frac-2neg clear-num add-log-exp
2×sqrt-div
1×frac-add associate-/l/
Counts
4 → 258
Calls
4 calls:
26.0ms
(/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x))
11.0ms
(/ 1.0 (sqrt (+ x 1.0)))
7.0ms
(/ 1.0 (sqrt x))
125.0ms
(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

series601.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x))
64.0ms
(/ 1.0 (sqrt (+ x 1.0)))
40.0ms
(/ 1.0 (sqrt x))
457.0ms
(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

simplify62.0ms

Algorithm
egg-herbie
Counts
270 → 270
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
012033694
150023295

prune494.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes35.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01512
11512

end0.0ms

sample874.0ms

Algorithm
intervals
Results
172.0ms1883×body640valid
160.0ms8004×body80nan
143.0ms1198×body1280valid
103.0ms3968×body80valid
42.0ms624×body320valid
15.0ms327×body160valid